Holistic medicine, or “holistic health”, is a belief that both the physical and mental aspects of life are closely connected and factor into the overall health and wellness of a person. Holistic health is usually associated with the topic of alternative medicine, but it is becoming more mainstream in this day and age.

The concept of holistic health is not new. Holism has been around for ages, but it has only been integrated into mainstream healthcare recently. There is a certain element of stubbornness in the medical field and sometimes it is slow to accept new ways of treatment or thinking. (http://allhealthcare.monster.com/training/articles/1930-what-is-holistic-health)

Holistic Health is actually an approach to life. Rather than focusing on illness or specific parts of the body, this ancient approach to health considers the whole person and how he or she interacts with his or her environment. It emphasizes the connection of mind, body, and spirit. The goal is to achieve maximum well-being, where everything is functioning the very best that is possible. With Holistic Health people accept responsibility for their own level of well-being, and everyday choices are used to take charge of one’s own health .( http://ahha.org/selfhelp-articles/holistic-health/)

Computer has become very important nowadays because it is very much accurate, fast and can accomplish many tasks easily. Otherwise to complete those tasks manually much more time is required. It can do very big calculations in just a fraction of a second. Moreover it can store huge amount of data in it. We also get information on different aspects using internet on our computer

Computers in schools will help the learners to comprehend the basic concepts better with the help of video or audio examples. Computers in higher learning institutions will help the professors and researchers to do their work very fast and in an efficient and better way and also help them to share the same knowledge with their other members of staff. Computers become a vital gadget in several sectors; railways, banking, electricity, telephone departments, shopping carts etc are just but a few of them. Computers are also used in the medical industry to help doctors in diagnosing the diseases quickly and efficiently

The Fox and the Grapes

One afternoon a fox was walking through the forest and spotted a bunch of grapes hanging from over a lofty branch. "Just the thing to quench my thirst," quoted the fox.

Taking a few steps back, the fox jumped and just missed the hanging grapes. Again the fox took a few paces back and tried to reach them but still failed.

Finally, giving up, the fox turned up his nose and said, "They're probably sour anyway," and proceeded to walk away.

Strong or WeakThere was a proud teak tree in the forest. He was tall and strong. There was a small herb next to the tree.

The teak tree said, “I am very handsome and strong. No one can defeat me”. Hearing this the herb replied, “Dear friend, too much pride is harmful. Even the strong will fall one day”.

The teak ignored the herb’s words. He continued to praise himself.

A strong wind blew. The teak stood firmly. Even when it rained, the teak stood strong by spreading its leaves.

At the same time, the herb bowed low. The teak made fun of the herb.

One day there was a storm in the forest. The herb bowed low. As usual the teak did not want to bow.

The storm kept growing stronger. The teak could no longer bear it. He felt his strength giving way.

He fell down. This was the end of the proud tree. When everything was calm the herb stood straight. He looked around. He saw the proud teak had fallen. Source: H&C

Basic math symbols

Symbol Symbol Name Meaning / definition Example

= equals sign equality 5 = 2+3

≠ not equal sign inequality 5 ≠ 4

> strict inequality greater than 5 > 4

< strict inequality less than 4 < 5

≥ inequality greater than or equal to 5 ≥ 4

≤ inequality less than or equal to 4 ≤ 5

( ) parentheses calculate expression inside first 2 × (3+5) = 16

[ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18

+ plus sign addition 1 + 1 = 2

− minus sign subtraction 2 − 1 = 1

± plus - minus both plus and minus operations 3 ± 5 = 8 and -2

∓ minus - plus both minus and plus operations 3 ∓ 5 = -2 and 8

* asterisk multiplication 2 * 3 = 6

× times sign multiplication 2 × 3 = 6

∙ multiplication dot multiplication 2 ∙ 3 = 6

÷ division sign / obelus division 6 ÷ 2 = 3

/ division slash division 6 / 2 = 3

– horizontal line division / fraction

mod modulo remainder calculation 7 mod 2 = 1

. period decimal point, decimal separator 2.56 = 2+56/100

ab power exponent 23 = 8

a^b caret exponent 2 ^ 3 = 8

√a square root √a · √a  = a √9 = ±3

3√a cube root 3√a · 3√a  · 3√a  = a 3√8 = 2

4√a fourth root 4√a · 4√a  · 4√a  · 4√a  = a 4√16 = ±2

n√a n-th root (radical) for n=3, n√8 = 2

% percent 1% = 1/100 10% × 30 = 3

‰ per-mille 1‰ = 1/1000 = 0.1% 10‰ × 30 = 0.3

ppm per-million 1ppm = 1/1000000 10ppm × 30 = 0.0003

ppb per-billion 1ppb = 1/1000000000 10ppb × 30 = 3×10-7

ppt per-trillion 1ppt = 10-12 10ppt × 30 = 3×10-10

Geometry symbols

Symbol Symbol Name Meaning / definition Example

∠ angle formed by two rays ∠ABC = 30º

measured angle ABC = 30º

spherical angle AOB = 30º

∟ right angle = 90º α = 90º

º degree 1 turn = 360º α = 60º

´ arcminute 1º = 60´ α = 60º59'

´´ arcsecond 1´ = 60´´ α = 60º59'59''

line infinite line

AB line segment line from point A to point B

ray line that start from point A

arc arc from point A to point B  = 60º

| perpendicular perpendicular lines (90º angle) AC | BC

|| parallel parallel lines AB || CD

≅ congruent to equivalence of geometric shapes and size ∆ABC ≅∆XYZ

~ similarity same shapes, not same size ∆ABC ~∆XYZ

Δ triangle triangle shape ΔABC ≅ΔBCD

|x-y| distance distance between points x and y | x-y | = 5

π pi constantπ = 3.141592654...is the ratio between the circumference and diameter of a circle

c = π·d = 2·π·r

rad radians radians angle unit 360º = 2π rad

grad grads grads angle unit 360º = 400 grad

Algebra symbols

Symbol Symbol Name Meaning / definition Example

x x variable unknown value to find when 2x = 4, then x = 2

≡ equivalence identical to

≜ equal by definition equal by definition

:= equal by definition equal by definition

~ approximately equal weak approximation 11 ~ 10

≈ approximately equal approximation sin(0.01) ≈ 0.01

∝ proportional to proportional to y ∝ x when y = kx, k constant

∞ lemniscate infinity symbol

≪ much less than much less than 1 ≪ 1000000

≫ much greater than much greater than 1000000 ≫ 1

( ) parentheses calculate expression inside first 2 * (3+5) = 16

[ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18

{ } braces set

⌊x⌋ floor brackets rounds number to lower integer ⌊4.3⌋= 4

⌈x⌉ ceiling brackets rounds number to upper integer ⌈4.3⌉= 5

x! exclamation mark factorial 4! = 1*2*3*4 = 24

| x | single vertical bar absolute value | -5 | = 5

f (x) function of x maps values of x to f(x) f (x) = 3x+5

(f ∘g) function composition (f ∘g) (x) = f (g(x)) f (x)=3x, g(x)=x-1 ⇒(f ∘g)(x)=3(x-1)

(a,b) open interval (a,b) = {x | a < x < b} x ∈ (2,6)

[a,b] closed interval [a,b] = {x | a ≤ x ≤ b} x ∈ [2,6]

∆ delta change / difference ∆t = t1 - t0

∆ discriminant Δ = b2 - 4ac

∑ sigma summation - sum of all values in range of series ∑ xi= x1+x2+...+xn

∑∑ sigma double summation

∏ capital pi product - product of all values in range of series ∏ xi=x1∙x2∙...∙xn

e e constant / Euler's number e = 2.718281828... e = lim (1+1/x)x , x→∞

γ Euler-Mascheroni  constant γ = 0.527721566...

φ golden ratio golden ratio constant

π pi constant

π = 3.141592654...

is the ratio between the circumference and diameter of a circle

c = π·d = 2·π·r

Linear Algebra Symbols

Symbol Symbol Name Meaning / definition Example

∙ dot scalar product a ∙ b

× cross vector product a × b

A⊗B tensor product tensor product of A and B A ⊗ B

inner product

[ ] brackets matrix of numbers

( ) parentheses matrix of numbers

| A | determinant determinant of matrix A

det(A) determinant determinant of matrix A

|| x || double vertical bars norm

A T transpose matrix transpose (AT)ij = (A)ji

A † Hermitian matrix matrix conjugate transpose (A†)ij = (A)ji

A * Hermitian matrix matrix conjugate transpose (A*)ij = (A)ji

A -1 inverse matrix A A-1 = I

rank(A) matrix rank rank of matrix A rank(A) = 3

dim(U) dimension dimension of matrix A rank(U) = 3

Probability and statistics symbols

Symbol Symbol Name Meaning / definition Example

P(A) probability function probability of event A P(A) = 0.5

P(A ∩ B) probability of events intersection

probability that of events A and B P(A∩B) = 0.5

P(A ∪ B) probability of events union

probability that of events A or B P(A∪B) = 0.5

P(A | B) conditional probability function

probability of event A given event B occured P(A | B) = 0.3

f (x) probability density function (pdf) P(a ≤ x ≤ b) = ∫ f (x) dx

F(x)cumulative distribution function (cdf)

F(x) = P(X ≤ x)

μ population mean mean of population values μ = 10

E(X) expectation value expected value of random variable X E(X) = 10

E(X | Y) conditional expectation

expected value of random variable X given Y E(X | Y=2) = 5

var(X) variance variance of random variable X var(X) = 4

σ2 variance variance of population values σ2 = 4

std(X) standard deviation standard deviation of random variable X std(X) = 2

σX standard deviation standard deviation value of random variable X σX  = 2

median middle value of random variable x

cov(X,Y) covariance covariance of random variables X and Y cov(X,Y) = 4

corr(X,Y) correlation correlation of random variables X and Y corr(X,Y) = 0.6

ρX,Y correlation correlation of random variables X and Y ρX,Y = 0.6

∑ summation summation - sum of all values in range of series

∑∑ double summation double summation

Mo mode value that occurs most frequently in population

MR mid-range MR = (xmax+xmin)/2

Md sample median half the population is below this value

Q1 lower / first quartile 25% of population are below this value

Q2median / second quartile

50% of population are below this value = median of samples

Q3 upper / third quartile 75% of population are below this value

x sample mean average / arithmetic mean x = (2+5+9) / 3 = 5.333

s 2 sample variance population samples variance

estimator s 2 = 4

s sample standard deviation

population samples standard deviation estimator s = 2

zx standard score zx = (x-x) / sx

X ~ distribution of X distribution of random variable X X ~ N(0,3)

N(μ,σ2) normal distribution gaussian distribution X ~ N(0,3)

U(a,b) uniform distribution equal probability in range a,b X ~ U(0,3)

exp(λ) exponential distribution f (x) = λe-λx , x≥0

gamma(c, λ) gamma distribution f (x) = λ c xc-1e-λx / Γ(c), x≥0

χ 2(k) chi-square distribution f (x) = xk/2-1e-x/2 / ( 2k/2 Γ(k/2) )

F (k1, k2) F distribution

Bin(n,p) binomial distribution f (k) = nCk pk(1-p)n-k

Poisson(λ) Poisson distribution f (k) = λke-λ / k!

Geom(p) geometric distribution f (k) =  p (1-p) k

HG(N,K,n) hyper-geometric distribution

Bern(p) Bernoulli distribution

Combinatorics Symbols

Symbol Symbol Name Meaning / definition Example

n! factorial n! = 1·2·3·...·n 5! = 1·2·3·4·5 = 120

nPk permutation 5P3 = 5! / (5-3)! = 60

nCk

combination 5C3 = 5!/[3!(5-3)!]=10

Set theory symbols

Symbol Symbol Name Meaning / definition Example

{ } set a collection of elements A = {3,7,9,14},B = {9,14,28}

A ∩ B intersection objects that belong to set A and set B A ∩ B = {9,14}

A ∪ B union objects that belong to set A or set B

A ∪ B = {3,7,9,14,28}

A ⊆ B subset subset has fewer elements or equal to the set {9,14,28} ⊆{9,14,28}

A ⊂ B proper subset / strict subset subset has fewer elements than the set {9,14} ⊂{9,14,28}

A ⊄ B not subset left set not a subset of right set {9,66} ⊄{9,14,28}

A ⊇ B superset set A has more elements or equal to the set B {9,14,28} ⊇{9,14,28}

A ⊃ B proper superset / strict superset

set A has more elements than set B {9,14,28} ⊃{9,14}

A ⊅ B not superset set A is not a superset of set B {9,14,28} ⊅{9,66}

2A power set all subsets of A

power set all subsets of A

A = B equality both sets have the same membersA={3,9,14},B={3,9,14},A=B

Ac complement all the objects that do not belong to set A

A \ B relative complement objects that belong to A and not to B

A = {3,9,14},B = {1,2,3},A-B = {9,14}

A - B relative complement objects that belong to A and not to B

A = {3,9,14},B = {1,2,3},A-B = {9,14}

A ∆ B symmetric difference objects that belong to A or B but not to their intersection

A = {3,9,14},B = {1,2,3},A ∆ B = {1,2,9,14}

A ⊖ B symmetric difference objects that belong to A or B but not to their intersection

A = {3,9,14},B = {1,2,3},A ⊖ B = {1,2,9,14}

a∈A element of set membership  A={3,9,14}, 3 ∈ A

x∉A not element of no set membership A={3,9,14}, 1 ∉ A

(a,b) ordered pair collection of 2 elements

A×B cartesian product set of all ordered pairs from A and B

|A| cardinality the number of elements of set A A={3,9,14}, |A|=3

#A cardinality the number of elements of set A A={3,9,14}, #A=3

aleph-null infinite cardinality of natural numbers set

aleph-one cardinality of countable ordinal numbers set

Ø empty set Ø = { } C = {Ø}

universal set set of all possible values

0natural numbers / whole numbers  set (with zero) 0 = {0,1,2,3,4,...} 0 ∈  0

1natural numbers / whole numbers  set (without zero) 1 = {1,2,3,4,5,...} 6 ∈  1

integer numbers set  = {...-3,-2,-1,0,1,2,3,...} -6 ∈ 

rational numbers set  = {x | x=a/b, a,b∈ } 2/6 ∈ 

real numbers set  = {x | -∞ < x <∞} 6.343434 ∈complex numbers set  = {z | z=a+bi, -∞<a<∞,      -

∞<b<∞} 6+2i ∈ 

Logic symbols

Symbol Symbol Name Meaning / definition Example

· and and x · y

^ caret / circumflex and x ^ y

& ampersand and x & y

+ plus or x + y

∨ reversed caret or x ∨ y

| vertical line or x | y

x' single quote not - negation x'

x bar not - negation x

¬ not not - negation ¬ x

! exclamation mark not - negation ! x

⊕ circled plus / oplus exclusive or - xor x ⊕ y

~ tilde negation ~ x

⇒ implies

⇔ equivalent if and only if (iff)

↔ equivalent if and only if (iff)

∀ for all

∃ there exists

∄ there does not exists

∴ therefore

∵ because / since

Calculus & analysis symbols

Symbol Symbol Name Meaning / definition Example

limit limit value of a function

ε epsilon represents a very small number, near zero ε → 0

e e constant / Euler's number e = 2.718281828... e = lim (1+1/x)x , x→∞

y ' derivative derivative - Lagrange's notation (3x3)' = 9x2

y '' second derivative derivative of derivative (3x3)'' = 18x

y(n) nth derivative n times derivation (3x3)(3) = 18

derivative derivative - Leibniz's notation d(3x3)/dx = 9x2

second derivative derivative of derivative d2(3x3)/dx2 = 18x

nth derivative n times derivation

time derivative derivative by time - Newton's notation

time second derivative derivative of derivative

Dx y derivative derivative - Euler's notation

Dx2

 y second derivative derivative of derivative

partial derivative ∂(x2+y2)/∂x = 2x

∫ integral opposite to derivation

∬ double integral integration of function of 2 variables

∭ triple integral integration of function of 3 variables

∮ closed contour / line integral

∯ closed surface integral

∰ closed volume integral

[a,b] closed interval [a,b] = {x | a ≤ x ≤ b}

(a,b) open interval (a,b) = {x | a < x < b}

i imaginary unit i ≡ √-1 z = 3 + 2i

z* complex conjugate z = a+bi → z*=a-bi z* = 3 + 2i

z complex conjugate z = a+bi → z = a-bi z = 3 + 2i

∇ nabla / del gradient / divergence operator ∇f (x,y,z)

vector

unit vector

x * y convolution y(t) = x(t) * h(t)

Laplace transform F(s) = {f (t)}

Fourier transform X(ω) =  {f (t)}

δ delta function

∞ lemniscate infinity symbol